论文标题
在非伴动歧管和liouville定理上的正标曲率曲率
Positive Scalar Curvature on Noncompact Manifolds and the Liouville Theorem
论文作者
论文摘要
Using minimal hypersurfaces, we obtain topological obstructions to admitting complete metrics with positive scalar curvature on a given class of non-compact n-manifolds with n less than 8. We show that the Liouville theorem for a locally conformally flat n-manifold of non-negative scalar curvature follows from the impossibility of there being a positive scalar curvature metric on its connect sum with the n-torus.随着Chodosh-Li的最新作品，在所有剩余案例中都证明了Liouville定理。最后，使用MOT而不是最小的Hypersurfaces，我们显示了这些结果的初始数据集版本，而显性能量标量出现而不是正标曲率。
Using minimal hypersurfaces, we obtain topological obstructions to admitting complete metrics with positive scalar curvature on a given class of non-compact n-manifolds with n less than 8. We show that the Liouville theorem for a locally conformally flat n-manifold of non-negative scalar curvature follows from the impossibility of there being a positive scalar curvature metric on its connect sum with the n-torus. With the recent work of Chodosh-Li, the Liouville theorem is now proved in all remaining cases. Finally, using MOTS instead of minimal hypersurfaces, we show an Initial Data Set version of these results with the Dominant Energy Scalar appearing instead of positive scalar curvature.
